Eva

Eva was the human wife of Sparda and mother of the twins Vergil and Dante. Little is known about Eva. She appears only as a photo on Dante's desk and as a voice in a flashback in the first Devil May Cry game.

Story
For Dante and Vergil's 8th birthday, she gave each of the boys one half of Sparda's Perfect Amulet. Afterwards, she was killed in a demon attack ordered by Mundus. She hid Dante underneath two stones and told him never to come out, no matter what. She gave her life for her sons. It is unclear where Vergil was at this time. Eva's death is most likely the event that shaped the paths Dante and Vergil took, causing Dante to fight demons and Vergil to search for Force Edge.

After Dante grew to adulthood, Trish was made by Mundus to look like Eva in order to manipulate Dante. Dante's lingering feelings for Eva are most clearly seen when Trish is saved by Dante despite her already betraying him.

Devil May Cry Volume 2
In a parallel universe that Dante and Beryl visit in which Mundus has virtually conquered the Human world, Eva supported her late husband's armies in resistance to Mundus's rule. It is also strongly implied that her emotional support after Sparda's fall was the only reason Mundus hadn't completed his conquest of the Human world. After hearing that story about this universe's Eva, Dante comments something along the lines of "she's the same in every universe."

DmC: Devil May Cry
In the relaunch of Devil May Cry, DmC: Devil May Cry, Eva is an angel. She fell in love with the demon and gave birth to twin sons,  and  before Mundus killed her and imprisoned Sparda.

Devil May Cry Volume 1
Eva is featured in a flashback in which she hides Dante and attempts to protect Vergil during the attack in which she was killed and Vergil was kidnapped. While subsequent works, particularly the Devil May Cry 3 Manga, have left this mostly intact, but have also omitted Vergil's presence at the site of Eva's murder thus leaving the details of Vergil's whereabouts at that time in mystery.>.

Viewtiful Joe
Mundus makes a cameo appearance in this game in which he delivers a rant and proclaims that "The real enemy was you, Eva!", implying that she had planned out his defeat in Devil May Cry 1 just before her death years in advance prior to the events of that game.

Bayonetta
Eva, and her husband Sparda are both referenced within the description of the Bracelet of Time accessory in Bayonetta, and it's sequel.

This would imply that not only was Eva her self a powerful Umbran Witch, with mastery over time control magic, but also participated in the battle against Mundus's Forces alongside Sparda.

Background
Eva is an alternate spelling for Eve, who in the Bible is said to have been the first woman created by God. Eve is infamous for having been tempted by the serpent to eat the Forbidden Fruit, which led to Adam and Eve being exiled from the Garden of Eden as punishment for succumbing to temptation. In some versions, she is a replacement for Adam after God's previous creation, Lilith, who abandoned Adam and became a demon.

Trivia

 * Eva's original death was different from the Devil May Cry 3 manga's depiction. In the novel, she was torn to pieces by vengeful demons right in front of Dante's eyes and Vergil was kidnapped by the demons, yet in the manga her death was altered slightly in that she told Dante to hide before dying in the demon's attack and Vergil's whereabouts are not explained.
 * Eva is very similar to Trisha Elric from Fullmetal Alchemist as they are the deceased mothers of the main characters and their physical appearance is revived by the main antagonists.